Recurrence plot: Difference between revisions

Revision as of 13:17, 9 January 2025

Revision as of 13:19, 9 January 2025

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:<math>\vec{x}(i) = (u(i), u(i+\tau), \ldots, u(i+\tau(m-1)),</math>

where <math>u(i)</math> is the time series (with <math>t = i \Delta t</math> and <math>\Delta t</math> the sampling time), <math>m</math> the embedding dimension and <math>\tau</math> the time delay. PhaseHowever, phase space reconstruction is not essential part of the recurrence plot (although often stated in literature), because it is based on phase space trajectories which could be derived from the system's variables directly (e.g., from the three variables of the [[Lorenz system]]) or from multivariate data.

The visual appearance of a recurrence plot gives hints about the dynamics of the system. Caused by characteristic behaviour of the phase space trajectory, a recurrence plot contains typical small-scale structures, as single dots, diagonal lines and vertical/horizontal lines (or a mixture of the latter, which combines to extended clusters). The large-scale structure, also called ''texture'', can be visually characterised by ''homogenous'', ''periodic'', ''drift'' or ''disrupted''. For example, the plot can show if the trajectory is strictly periodic with period <math>T</math>, then all such pairs of times will be separated by a multiple of <math>T</math> and visible as diagonal lines.